Compton Scattering Calculator

Formula and assumptions

This Compton scattering calculator helps you see how a photon changes when it bounces off an electron. It computes the Compton wavelength shift, the scattered wavelength, and the before/after photon energy based on your input wavelength or energy and the scattering angle. In short, it translates a classic quantum interaction into numbers you can visualize, which is especially helpful for students, lab planning, and quick checks.

The key idea is that light behaves like a particle with momentum. When a photon collides with an electron, some energy and momentum transfer to the electron, causing the photon to emerge with a longer wavelength and lower energy. The shift depends only on the scattering angle: Δλ = (h / m_ec)(1 − cos θ). The prefactor h / (m_ec) is the Compton wavelength of the electron, and the angle term tells you how much the photon is deflected. Once you know the shift, the scattered wavelength is λ′ = λ + Δλ, and the energy follows from E = hc / λ.

To use the calculator, start by entering the incident photon wavelength or energy, then choose the scattering angle. The tool accepts common X-ray and gamma ray values but works for any wavelength you provide. Click Calculate to see the wavelength shift, the new wavelength, and the corresponding energy after scattering. If you switch input modes, the calculator updates automatically so you can compare energy and wavelength perspectives side by side.

Compton scattering shows up in medical imaging, radiation physics, materials analysis, and astrophysics. It helps explain how X-rays lose energy as they pass through tissue, why gamma-ray detectors measure scattered photons, and how high-energy light interacts with electrons in space. While this tool uses the standard free-electron model, it captures the essential physics for many educational and practical settings.

This calculator assumes the initial electron is at rest and unbound. Bound electrons, relativistic electrons, or Klein–Nishina cross-section effects are out of scope here, but the simple formula is accurate for many X-ray setups and classroom problems.